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1、JournalofPhysicsCommunicationsPAPER•OPENACCESSRelatedcontent-Combinedfew-bodyandmean-fieldmodelSolutionofthelogarithmicSchrödingerequationfornucleiDHove,EGarrido,PSarrigurenetal.withaCoulombpotential-Advancedmulticonfigurationmethodsforcomplexatoms:PartI—Energiesandwavef
2、unctionsTocitethisarticle:TCScottandJShertzer2018J.Phys.Commun.2075014CharlotteFroeseFischer,MichelGodefroid,TomasBrageetal.-SchwartzinterpolationfortheCoulombpotentialKMDunseath,J-MLaunay,MTerao-Viewthearticleonlineforupdatesandenhancements.Dunseathetal.Thiscontentwasdo
3、wnloadedfromIPaddress61.174.132.238on14/08/2018at08:47J.Phys.Commun.2(2018)075014https://doi.org/10.1088/2399-6528/aad302PAPERSolutionofthelogarithmicSchrödingerequationwithaCoulombOPENACCESSpotentialRECEIVED5June2018TCScott1,2andJShertzer3REVISED1NearPte.Ltd,15BeachRoad
4、,189677,Singapore4July20182InstitutfürPhysikalischeChemie,RWTHAachenUniversity,D-52056Aachen,GermanyACCEPTEDFORPUBLICATION3DepartmentofPhysics,CollegeoftheHolyCross,1CollegeSt,Worcester,MA01610,UnitedStatesofAmerica12July2018E-mail:tcscott@gmail.comPUBLISHED24July2018Key
5、words:logarithmicSchrödingerequation,Gaussons,finiteelementmethodsOriginalcontentfromthisworkmaybeusedunderthetermsoftheCreativeAbstractCommonsAttribution3.0licence.ThenonlinearlogarithmicSchrödingerequation(logSE)appearsinmanybranchesoffundamentalAnyfurtherdistributionof
6、physics,rangingfrommacroscopicsuperfluidstoquantumgravity.Weconsiderhereamodelthisworkmustmaintainattributiontotheproblem,inwhichthelogSEincludesanattractiveCoulombinteraction.Wederiveananalyticalauthor(s)andthetitleofsolutionforthegroundstateenergyandwavefunctionasafunct
7、ionofthestrengthofthelogarithmicthework,journalcitationandDOI.interaction.WedevelopaniterativefiniteelementmethodtosolvetheCoulombiclogSEforthesphericallysymmetricstates.Thegroundstateresultsagreewiththeexactsolutiontobetterthanone108partin10.Theexcitedstates(n>1)areconve
8、rgedtobetterthanonepartin10.Wealsoconstructaremarkablysimplevariationalwavefunction,consistingofasumofG
